# Can "round" refer to an ellipse, in the case that ratio of circumference to length is 3:1?

As quoted in Eruvin 14a, from Kings I 7:23, we know that Shlomo's pool was round, measuring 10 across and 30 around. There have been discussions about how the ratio of these (3:1) is only an approximation to pi, or that it deals only with significant figures.

Are there any sources that deal with the possibility that the pool was not circular, but rather an ellipse? A major axis of 5 and minor axis of 4.543 would give a circumference of 30. Are these any other places where sources discuss elliptical shapes as ways of resolving a seeming contradiction?

Of course, this is separate from the discussion in the daf regarding the shape of the 3D pool. The calculation of volume would have to change to accommodate the difference in area of the top (ellipse would have an area even smaller than the circle).

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– Dov
Sep 21, 2020 at 16:42
• I'm not holding in the Hebrew math terms but maybe check out daf-yomi.com/Data/UploadedFiles/DY_Item/21447-sFile.pdf page 5. Sep 21, 2020 at 20:13
• Some Meforshim explain that the reason for the pasuk telling us the ratio of the pool is to provide a halachic approximation for pi. Otherwise we'd just figure it out ourselves. If it was elliptical, though, what would be the point? Sep 22, 2020 at 1:12
• Is assuming an imprecisely specified ellipse any better than assuming an imprecise circumference? Sep 22, 2020 at 1:50
• An ellipse would lead to other calculations regarding the shape of the walls from top to bottom than the end of the discussion in the Gemara (of 3 straight and 2 curved). The long article linked below, plus the reference from it that I've identified indicate how the volume calculations would shift. Sep 22, 2020 at 15:43